A true 3-D simulation of an injection moulding process or a metal casting process involves a system of up to several hundred thousands of equations. Progress has been made in the past to improve the efficiency of the simulation methods to cope with these complex calculations. With optimized software and the processing power of modern workstations such simulations can be performed in a workplace, i.e. the results are obtained fast enough to be suitable outside the purely scientific research area and can be applied by engineers in research and development departments, foundries and manufacturers of injection moulded articles.
When particles, such as fibres, are added to the polymer composition, and the orientation distribution of the fibres needs to be described, the simulation and belonging equation set becomes significantly more complex. True 3-D simulation of such a process has hitherto not been introduced successfully on the workplace since the complexity of the simulation would not allow acceptable results on present day workstations, since either the computation time would be too long, or the accuracy of the simulation would be inadequate.
In fibre reinforced parts it is often crucial for development engineers to have a description of the fibre orientation distribution to be able to predict tension and warping aspects of the component. Typically fibres are used to improve the mechanical properties of plastic parts. But then the (thermo-) mechanical properties (like thermal expansion, strength and stiffness) depend on the orientation of the fibres.
The use of injection moulded plastic components has steadily increased in many industries in recent years. Manufacturers of electronic equipment, consumer goods, medical equipment, and automotive parts are producing more and more of their products and components used in their products out of plastics than ever before.
Injection moulded fibre reinforced parts are replacing structural metallic components because they offer an improved strength/weight ratio, durability, component integration and lower costs.
At the same time, competitive pressures are driving manufacturers in the plastic injection moulding industry to find new methods to optimize the designs in order to better match the designs to the production process. When the need for component or mould configuration modifications are discovered late in the design development process, the delay and associated costs to implement the necessary changes are significantly higher than in earlier stages of the design development stages.
Companies that want to ensure that their components are producible and will perform optimally would like to use computer aided engineering techniques to simulate or model the complex flows and resulting fibre orientation in an injection mould, in order to understand better the manufacturing process and integrate this knowledge into component design, early in the design phase.
There are a number of factors that should be considered when designing an injection mould for a fibre reinforced component and for the fibre reinforced component which is to be produced therein. Parameters such as the overall component geometry, minimum and maximum wall thicknesses, number and location of gates in the mould through which the liquid polymer and fibre suspension is injected, number and location of vents in the mould through which gas in the cavity escapes, polymer composition and properties, fibre properties and quantity, shrinkage, allowances and fibre orientation distribution are a few. Due to the closely interrelated relationship, component and mould design cannot reliably be based purely on form and function of the end component, but should also consider the effects of the manufacturing process.
Computer aided engineering simulation can be used advantageously to provide design and manufacturing engineers with visual and numerical feedback as to what is likely to happen inside the mould cavity during the injection moulding process, allowing them to better understand and predict the behaviour of contemplated component designs so that the traditional, costly trial and error approach to manufacturing can be eliminated substantially. The use of computer aided engineering simulation facilitates optimizing component designs, mould designs, and manufacturing processing parameters during the design phase, where necessary changes can be implemented readily, with the least cost and impact on schedule.
The application of CAE simulation techniques within the engineering process for fibre reinforced components encompasses (i) a simulation of the “injection moulding” manufacturing process including the computation of fluid flow and heat transfer and (ii) stress & strength (and possibly durability) calculations, all performed on the macroscopic level, for these components to determine their functional mechanical properties under external loads. Both types of simulation require suitable material models describing the properties of the polymer material containing the immersed fibres in liquid as well as in the solid state.
The length scale on the macroscopic level are determined by the linear dimensions (overall size, wall thicknesses etc.) of the component geometry typically varying in the range of a few mm up to cm. The dimensions of the computational cells have to resolve the macroscopic length scales with sufficient accuracy, therefore they are typically up to one order of magnitude smaller than the smallest macroscopic dimension. As the typical dimensions of the immersed fibres in short-fibre reinforced parts are one or two orders of magnitude below the typical dimensions of the macroscopic computational cells, the fibre properties, which are relevant to the modelling of the macroscopic material behaviour are described by a statistical approach. For short-fibre reinforced materials relevant macroscopic properties are: (a) the volume concentration, which is typically (approximately) constant over the whole part, and (b) the local distribution of the fibre orientation (FO) within each computational cell, which typically varies significantly across the part geometry. (Further details of this topic are discussed in the sections 1.1 and 1.2 of the detailed description.)
A simplified and for practical purposes appropriate description of the statistical distribution of the local FO is provided by means of the low (i.e. 2nd and 4th) order moments of the corresponding distribution function. Because of their mathematical structure these moments are denoted as orientation tensors (of 2nd and 4th order respectively). Within the framework of CAE simulation for fibre reinforced components the 4th order tensors are needed to predict the rheological as well as the mechanical properties of the fibre reinforced material on the macroscopic level, as these are 4th order tensor properties. The 2nd order FO tensor is a real-valued symmetric 3×3 matrix having unit trace, therefore only 5 of its 9 components are independent. The number of independent components of the 4th order FO tensor is reduced from 34=81 to 15 by means of (total) symmetry.
The mathematical model describing the FO distribution in terms of its moments is significantly simplified by means of an approximate computation of the 4th order orientation tensor in terms of the 2nd order tensor in terms of a closure relation. A closure relation provides the mathematical description of such a computational scheme in terms of a function, and the related computational procedure is denoted as “closure approximation” if a closure relation is only approximately valid under specific assumptions. The approach using only the 2nd order FO tensor together with some closure approximation leads to a model of “Folgar-Tucker” type to simulate the evolution of the 2nd order FO tensor in time and space during the mould filling process (see sections 2.2 to 2.5 of the detailed description for details).
The document “Glass fibre orientation within injection moulded automotive pedal—Simulation and experimental studies, B. R. Whiteside et Al, Plastics, Rubber and Composites, 2000, Volume 29, No. 1” discloses a method for modelling the fibre orientation distribution within a reinforced thermoplastic article using on the asymmetric thermoplastic flow and analysis containing a fibre orientation prediction algorithm. The software approximated a three-dimensional model using a two-dimensional finite element mesh consisting of linear triangular elements. Flow fields were calculated using the generalized Hele-Shaw approximation and a variation of the Folgar-Tucker equation to calculate fibre orientation. Fibre orientation, temperature and viscosity calculations were performed using a finite difference technique over 19 laminates through the “thickness” of each element in order to produce a three dimensional solution. However, it is important to note that this system could not be described as truly three-dimensional because the model cannot simulate velocity components in the out of plane direction (a limitation of the Hele-Shaw approximation). The method described in this document would, when adapted to true three-dimensional simulation, result in a unstable and too much processing power consuming simulation that could not be used in the workplace of e.g. development engineers.